Electric Potential at Point A between Charges q and q

To find the electric potential at point A, which is located midway between the two charges q and q, we need to consider the contributions from each charge individually and then sum them up.

Given:
- Four electric charges: q, q, -q, and -q
- The charges are placed at the corners of a square of side 2L

Breaking down the solution into headings and key pointers:

1. Identify the Charges and their Positions:
- We have four charges: q, q, -q, and -q
- The charges are placed at the corners of a square of side 2L

2. Calculate the Electric Potential Contribution from each Charge:
- The electric potential at a point due to a charge q can be calculated using the formula V = k * q / r, where k is the electrostatic constant and r is the distance from the charge to the point.

3. Calculate the Distance from each Charge to Point A:
- Point A is located midway between the two charges q and q.
- The distance from each charge q to point A is L, as it is the side length of the square divided by 2.

4. Consider the Contributions from Charges q and -q to the Electric Potential at Point A:
- The electric potential at point A due to the charges q and -q can be calculated separately using the formula V = k * q / r.
- The distance r from each charge to point A is L.
- The electric potential due to charge q at point A is V_q = k * q / L.
- The electric potential due to charge -q at point A is V_-q = k * (-q) / L = -k * q / L.

5. Sum up the Electric Potential Contributions from Charges q and -q:
- The net electric potential at point A is the sum of the contributions from charges q and -q.
- V_A = V_q + V_-q = k * q / L - k * q / L = 0.

6. Conclusion:
- The electric potential at point A, located midway between the two charges q and q, is zero.
- This means that the contributions from the positive and negative charges cancel each other out, resulting in no net electric potential at that point.

By following these steps, we have determined that the electric potential at point A is zero.

Ans-2q/4πεoL[2(√5-1) /√5]